{"id":230491,"date":"2025-06-09T15:37:59","date_gmt":"2025-06-09T15:37:59","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230491"},"modified":"2025-06-09T15:38:01","modified_gmt":"2025-06-09T15:38:01","slug":"the-area-of-the-shaded-part-of-the-figure-below-can-be-determined-in-different-ways","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/09\/the-area-of-the-shaded-part-of-the-figure-below-can-be-determined-in-different-ways\/","title":{"rendered":"The area of the shaded part of the figure below can be determined in different ways."},"content":{"rendered":"\n<p>The area of the shaded part of the figure below can be determined in different ways. Use the drop-down menus to explain how to find the area by decomposing the figure into rectangles or trapezoids. 5 in. 2 in. 2 in. 5 in. Click the arrows to choose an answer from each menu. The figure can be decomposed into two 5 in. by 1.5 in. and two 2 in. by 1.5 in. rectangles, or the figure can be decomposed into 4 trapezoids with heights of Choose\u2026 in. and bases of Choose\u2026 in. and 5 in. Using either method, the total area of the shaded figure is 21 square inches.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To determine the area of the shaded part of the figure, we can analyze it in two different ways\u2014either by decomposing it into rectangles or into trapezoids. Based on the dimensions provided:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>5 in.<\/strong><\/li>\n\n\n\n<li><strong>2 in.<\/strong><\/li>\n\n\n\n<li><strong>2 in.<\/strong><\/li>\n\n\n\n<li><strong>5 in.<\/strong><\/li>\n<\/ul>\n\n\n\n<p>And given that the total area is <strong>21 square inches<\/strong>, here\u2019s how to proceed:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Correct Drop-down Answers:<\/strong><\/h3>\n\n\n\n<p><strong>The figure can be decomposed into two 5 in. by 1.5 in. and two 2 in. by 1.5 in. rectangles<\/strong>,<br>or<br><strong>the figure can be decomposed into 4 trapezoids with heights of 1.5 in. and bases of 2 in. and 5 in.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation<\/strong><\/h3>\n\n\n\n<p>To find the area of the shaded figure, we can use two effective decomposition strategies: breaking it into <strong>rectangles<\/strong> or into <strong>trapezoids<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Method 1: Decomposing into Rectangles<\/strong><\/h3>\n\n\n\n<p>According to the figure\u2019s dimensions, the shape includes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Two <strong>5-inch by 1.5-inch<\/strong> rectangles<\/li>\n\n\n\n<li>Two <strong>2-inch by 1.5-inch<\/strong> rectangles<\/li>\n<\/ul>\n\n\n\n<p>To compute the total area, find the area of each rectangle and sum them up:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Area of each 5 in. \u00d7 1.5 in. rectangle = 5 \u00d7 1.5 = <strong>7.5 square inches<\/strong><\/li>\n\n\n\n<li>Area of each 2 in. \u00d7 1.5 in. rectangle = 2 \u00d7 1.5 = <strong>3 square inches<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Now, total area:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2 \u00d7 7.5 = 15 square inches<\/li>\n\n\n\n<li>2 \u00d7 3 = 6 square inches<\/li>\n\n\n\n<li>Total area = 15 + 6 = <strong>21 square inches<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Method 2: Decomposing into Trapezoids<\/strong><\/h3>\n\n\n\n<p>Alternatively, the figure can be split into <strong>four trapezoids<\/strong>, each with:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>height of 1.5 inches<\/strong><\/li>\n\n\n\n<li><strong>Bases of 2 inches and 5 inches<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Use the area formula for a trapezoid:Area=12\u00d7(Base1+Base2)\u00d7Height\\text{Area} = \\frac{1}{2} \\times (\\text{Base}_1 + \\text{Base}_2) \\times \\text{Height}Area=21\u200b\u00d7(Base1\u200b+Base2\u200b)\u00d7Height=12\u00d7(2+5)\u00d71.5=12\u00d77\u00d71.5=5.25&nbsp;square&nbsp;inches= \\frac{1}{2} \\times (2 + 5) \\times 1.5 = \\frac{1}{2} \\times 7 \\times 1.5 = 5.25\\ \\text{square inches}=21\u200b\u00d7(2+5)\u00d71.5=21\u200b\u00d77\u00d71.5=5.25&nbsp;square&nbsp;inches<\/p>\n\n\n\n<p>Each trapezoid is <strong>5.25 square inches<\/strong>, and with 4 trapezoids:4\u00d75.25=21&nbsp;square&nbsp;inches4 \\times 5.25 = 21\\ \\text{square inches}4\u00d75.25=21&nbsp;square&nbsp;inches<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>Both methods yield the same total shaded area of <strong>21 square inches<\/strong>, verifying the accuracy of the decomposition.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-754.jpeg\" alt=\"\" class=\"wp-image-230492\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The area of the shaded part of the figure below can be determined in different ways. Use the drop-down menus to explain how to find the area by decomposing the figure into rectangles or trapezoids. 5 in. 2 in. 2 in. 5 in. Click the arrows to choose an answer from each menu. The figure [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-230491","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230491","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=230491"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230491\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230491"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230491"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230491"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}